Scientific notation is a short way to write very large or very small numbers. You write the number as a value from 1 up to (but not including) 10, times a power of 10. For example, 4,500,000 in scientific notation is , and 0.00032 is . Before this lesson: You should know powers of 10…
A cube root of a number is the value you multiply by itself three times to get that number. The cube root of 27 is 3, because . We write it as . Unlike square roots, negative numbers have cube roots, so . Before this lesson: You should know cubes from Exponents and the ideas…
Simple interest is money you earn on savings, or pay on a loan, based only on the starting amount. Use the formula . Multiply the principal by the yearly interest rate , written as a decimal, and the time in years. For example, $500 at 4% for 3 years earns , or $60. Before this…
Percent word problems use percents to find real prices. For a discount, find the percent of the price and subtract it. For sales tax, a tip or a markup, find the percent and add it. For example, a $40 shirt that is 25% off costs 40 − 10 = $30, because 25% of 40 is…
Percent change tells how much an amount went up or down, compared to where it started. Subtract to find the change, divide by the original amount, then multiply by 100. If a price goes from $50 to $60, the change is $10, and 10 ÷ 50 = 0.20. That is a 20% increase. Before this…
Unit conversions change a measurement from one unit to another, like feet to inches or minutes to hours. Multiply by a conversion factor, which is a fraction equal to 1, such as . Put the unit you want on top, so the old unit cancels. For example, . Before this lesson: You should know how…
A unit rate tells how much of one thing there is for exactly 1 unit of another, like 60 miles per hour or $3 per pound. To find a unit rate, divide the first amount by the second amount. For example, $12 for 4 pounds of apples is 12 ÷ 4 = $3 per pound….
A ratio compares two amounts. If a shelter has 3 cats and 5 dogs, the ratio of cats to dogs is 3 to 5. You can write it as 3 to 5, 3:5 or . Equivalent ratios make the same comparison, like 3:5 and 6:10. To find equivalent ratios, multiply or divide both numbers by…
Converting fractions and decimals works in both directions. To change a fraction to a decimal, divide the top by the bottom: . To change a decimal to a fraction, write its digits over 10, 100 or 1,000 and simplify: . Some fractions never end, like Before this lesson: You should know how to simplify fractions…
Mixed numbers and improper fractions are two ways to write an amount bigger than 1. A mixed number has a whole number and a fraction, like . An improper fraction has a top number that is at least as big as the bottom, like . To change , multiply 2 by 4 and add 3…
